Download each segment that forms a polygon

6-1
___________________________: each segment that forms a polygon
___________________________: the common endpoint of two sides
____________________: a segment that connects any two nonconsecutive vertices
Number of Sides
3
4
5
6
7
8
9
10
12
n
Name of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
__________________________: a polygon that is both equilateral and equiangular [all sides are the same length
and all angles are the same measure]
__________________________: a polygon in which a diagonal can be drawn such that part of the diagonal
contains points in the exterior of the polygon
 draw a concave polygon:
__________________________: a polygon in which no diagonal contains points in the exterior of the polygon
-- a regular polygon is always convex
 draw a convex polygon:
Let’s work out together how many degrees are in the interior of a convex polygon...
…I’ve drawn in all possible diagonals from one vertex of the polygon.
…now you fill in the blanks in the table.
Triangle:
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon
Quadrilateral:
Number of Sides
Pentagon:
Number of Triangles
Hexagon:
Sum of Interior Angle Measures
1 x 180° = 180°
Polygon Exterior Angle Sum Theorem:
The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360°.
-- guess what?!? this works no matter how many sides the polygon has
Ex. 1: Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.
A.
B.
C.
D.
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
Ex. 2: Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
A.
B.
C.
_________________
_________________
_________________
_________________
_________________
_________________
Ex. 3:
A. Find the sum of the interior angle measures of a convex heptagon.
a heptagon has _____ sides, so the sum of the interior angle measures is (n – 2) x 180°
B. Find the measure of each interior angle of a regular 16-gon.
a 16-gon has _____ sides, so the sum of the interior angle measures is (n – 2) x 180°
each angle is _________°/16 = ________°
C. Find the measure of each interior angle of pentagon ABCDE.
the sum of a pentagon’s interior angles is _______°
m A=
35c + ______ + ______ + ______ + ______ = 540
m B=m E=
______ = 540
m C=m D=
c = ______
Ex. 4:
A. Find the measure of each exterior angle of a regular 20-gon.
remember…the measures of the exterior angles of any polygon add to ______°
…so each one in a regular 20-gon is ______°/_____ = _____°
B. Find the value of b in polygon FGHJKL.
_______ + _______ + _______ + _______ + _______ + _______ = 360°
_________ = 360°
b = _____
Ex. 5: These are paper star decorations for a 4th of July Party…what is the measure of
indicate that there is a regular pentagon in the center of the star?
1 is an __________________ angle of the regular __________________
remember…the measures of the exterior angles of any polygon add to ______°
…so each one in a regular pentagon is ______°/____ = ______°
1 if the tick marks